(5x+1)(x+3)-8=5(x+1)(x+2)

Solution for (5x+1)(x+3)-8=5(x+1)(x+2) equation:

Simplifying
(5x + 1)(x + 3) + -8 = 5(x + 1)(x + 2)

Reorder the terms:
(1 + 5x)(x + 3) + -8 = 5(x + 1)(x + 2)

Reorder the terms:
(1 + 5x)(3 + x) + -8 = 5(x + 1)(x + 2)

Multiply (1 + 5x) * (3 + x)
(1(3 + x) + 5x * (3 + x)) + -8 = 5(x + 1)(x + 2)
((3 * 1 + x * 1) + 5x * (3 + x)) + -8 = 5(x + 1)(x + 2)
((3 + 1x) + 5x * (3 + x)) + -8 = 5(x + 1)(x + 2)
(3 + 1x + (3 * 5x + x * 5x)) + -8 = 5(x + 1)(x + 2)
(3 + 1x + (15x + 5x2)) + -8 = 5(x + 1)(x + 2)

Combine like terms: 1x + 15x = 16x
(3 + 16x + 5x2) + -8 = 5(x + 1)(x + 2)

Reorder the terms:
3 + -8 + 16x + 5x2 = 5(x + 1)(x + 2)

Combine like terms: 3 + -8 = -5
-5 + 16x + 5x2 = 5(x + 1)(x + 2)

Reorder the terms:
-5 + 16x + 5x2 = 5(1 + x)(x + 2)

Reorder the terms:
-5 + 16x + 5x2 = 5(1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
-5 + 16x + 5x2 = 5(1(2 + x) + x(2 + x))
-5 + 16x + 5x2 = 5((2 * 1 + x * 1) + x(2 + x))
-5 + 16x + 5x2 = 5((2 + 1x) + x(2 + x))
-5 + 16x + 5x2 = 5(2 + 1x + (2 * x + x * x))
-5 + 16x + 5x2 = 5(2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
-5 + 16x + 5x2 = 5(2 + 3x + x2)
-5 + 16x + 5x2 = (2 * 5 + 3x * 5 + x2 * 5)
-5 + 16x + 5x2 = (10 + 15x + 5x2)

Add '-5x2' to each side of the equation.
-5 + 16x + 5x2 + -5x2 = 10 + 15x + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-5 + 16x + 0 = 10 + 15x + 5x2 + -5x2
-5 + 16x = 10 + 15x + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-5 + 16x = 10 + 15x + 0
-5 + 16x = 10 + 15x

Solving
-5 + 16x = 10 + 15x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-15x' to each side of the equation.
-5 + 16x + -15x = 10 + 15x + -15x

Combine like terms: 16x + -15x = 1x
-5 + 1x = 10 + 15x + -15x

Combine like terms: 15x + -15x = 0
-5 + 1x = 10 + 0
-5 + 1x = 10

Add '5' to each side of the equation.
-5 + 5 + 1x = 10 + 5

Combine like terms: -5 + 5 = 0
0 + 1x = 10 + 5
1x = 10 + 5

Combine like terms: 10 + 5 = 15
1x = 15

Divide each side by '1'.
x = 15

Simplifying
x = 15